Time-frequency analysis for non-linear and non-stationary signals is extraordinarily challenging. To capture the changes in these types of signals, it is necessary for the analysis methods to be local, adaptive and stable. In recent years, decomposition based analysis methods were developed by different researchers to deal with non-linear and non-stationary signals. These methods share the feature that a signal is decomposed into finite number of components on which the time-frequency analysis can be applied. Differences lie in the strategies to extract these components: by iteration or by optimization. However, considering the requirements of being local, adaptive and stable, neither of these decompositions are perfectly satisfactory. Motivated to find a local, adaptive and stable decomposition of a signal, this thesis presents Adaptive Local Iterative Filtering (ALIF) algorithm. The adaptivity is obtained having the filter lengths being determined by the signal itself. The locality is ensured by the filter we designed based on a PDE model. The stability of this algorithm is shown and the convergence is proved. Moreover, we also propose a local definition for the instantaneous frequency in order to achieve a completely local analysis for non-linear and non-stationary signals. Examples show that this decomposition really helps in both simulated data analysis and real world application.

Made available in DSpace on 2014-12-17T14:08:53Z (GMT). No. of bitstreams: 1 LigiaSC_DISSERT.pdf: 4461688 bytes, checksum: f25524320fdb2202381f0125f35cf61f (MD5) Previous issue date: 2011-02-07 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / The Potengi river estuary is located in the region of Natal (RN, Brazil), comprising a population of approximately 1,000,000 inhabitants. Besides the dominant urban presence, the estuary has fragments of mangrove forest. The objective of this study is to determine the aliphatic hydrocarbons found in the bottom sediments of this estuary, identifying their levels, distribution and their possible origins through the diagnostic rates, indexes and results comparisons with the local anthropic and natural characteristics. The samples were obtained according to a plan that allowed sampling of the estuary up to 12 km upstream from it as mounth. 36 stations were selected, grouped into 12 cross sections through the course of the river and spaced on average by 1 km. Each section consisted of three stations: the right margin, the deepest point and the left margin. The hydrocarbon n-alkanes from C10 to C36, the isoprenoids pristane and phytane, the unresolved complex mixture (UCM) and the total resolved hydrocarbons were analyzed by gas chromatography. N-alkanes, pristane, phytane and UCM were detected only at some stations. In the other, the concentration was below the detection limit defined by the analytical method (0.1 mg / kg), preventing them from being analyzed to determine the origin of the material found. By using different parameters, the results show that the estuary receives both the input of petrogenic hydrocarbons, but also of biogenic hydrocarbons, featuring a mixture of sources and relatively impacted portions. Based on the characteristics and activities found in the region, it is possible to affirm that petrogenic sources related to oil products enter the estuary via urban runoff or boats traffic, boat washing and fueling. Turning to the biogenic source, the predominant origin was terrestrial, characterized by vascular plants, indicating contribution of mangrove vegetation. It was evident the presence of, at specific points in the estuary, hydrocarbon pollution, and, therefore is recommended the adoption of actions aimed at interrupting or, at least, mitigating the sources potentially capable of damp petrogenic hydrocarbons in the estuary studied. / O estu?rio do rio Potengi est? inserido na regi?o da Grande Natal (RN, Brasil), que compreende uma popula??o de aproximadamente 1.000.000 de habitantes. Al?m da presen?a urbana dominante, este estu?rio mant?m fragmentos de floresta de manguezal. O objetivo deste estudo foi determinar os hidrocarbonetos alif?ticos em sedimentos de fundo do estu?rio, identificando os n?veis, distribui??o e suas poss?veis origens atrav?s dos ?ndices, raz?es diagn?sticas e compara??o dos resultados com as caracter?sticas antr?picas e naturais vigentes no local. As amostras foram obtidas obedecendo a um plano de amostragem que permitiu uma varredura desde a foz do estu?rio at? 12 km a montante. Foram escolhidas 36 esta??es, agrupadas em 12 se??es transversais ao curso do rio espa?adas, em m?dia, por 1 km. Cada se??o era composta de tr?s esta??es: margem direita, ponto mais profundo e margem esquerda. Atrav?s da cromatografia gasosa, foram analisados os hidrocarbonetos n-alcanos do C10 ao C36, os isopren?ides pristano e fitano, a mistura complexa n?o resolvida (MCNR), al?m dos resolvidos totais. Foram detectados n-alcanos, pristano, fitano e MCNR apenas em algumas esta??es. Nas demais, a concentra??o foi inferior ao limite de detec??o estabelecido pelo m?todo anal?tico (0,1 mg/kg), impossibilitando-as de serem analisadas para a determina??o da origem do material encontrado. Atrav?s da utiliza??o de diferentes par?metros, os resultados demonstram que o estu?rio recebe tanto o aporte de hidrocarbonetos petrog?nicos, como tamb?m de hidrocarbonetos biog?nicos, caracterizando uma mistura de fontes e ?reas mais ou menos impactadas. Com base nas caracter?sticas e atividades encontradas na regi?o, podemos afirmar que as fontes petrog?nicas relacionam-se a derivados de petr?leo que entram no estu?rio atrav?s do escoamento urbano ou pelo tr?fego, lavagem e abastecimento de embarca??es; com rela??o ? fonte biog?nica, predominou origem terrestre caracterizado por plantas vasculares, indicando contribui??o da vegeta??o de mangue presente no local. Fica evidenciado o registro, em pontos espec?ficos do estu?rio, da polui??o por hidrocarbonetos, sendo recomendada a tomada de medidas objetivando a interrup??o ou, pelo menos, a atenua??o das fontes potencialmente capazes de aportar hidrocarbonetos petrog?nicos no estu?rio estudado